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Abstract

An extended relational algebra has been developed. This extended algebra
is suitable for reduction of expressions written in the natural quantifier
language COOL. The algebra consists of conventional operations
plus a group select, a subgroup select and possibility join operation.
The group select operation selects each group of related tuples where a
quantity of the group obeys a condition. The subgroup-select operation
selects each group of related tuples where a quantity of a subgroup of
the group obeys a condition. The possibility join of relation R1 with
relation R2 regenerates relation R1 but with each tuple having a logical
attribute p concatenated, with p true where the R1 tuple could have been
joined to an R2 tuple, otherwise p false. Generalized algebra routines
for generalized COOL expressions are presented.

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